Optimal Reactive Power Dispatch with Discrete Controllers Using a Branch-and-Bound Algorithm A Semidefinite Relaxation Approach
ABSTARCT :
Recently, several convex relaxations have been successfully applied to solve the AC optimal power flow (OPF) problem, which has caught the attention of the research community. Among these relaxations, a relaxation based on semidefinite programming (SDP) stands out. Accordingly, in this work a methodology to solve the optimal reactive power dispatch (ORPD) in electric power systems (EPS), considering discrete controllers, is proposed. Discrete controllers, such as the tap position of on-load tap changing (OLTC) transformers and switchable reactive shunt compensation, are optimized by the proposed method.A semidefinite relaxation (SDR) of the ORPD problem and a branch-and-bound (B&B) algorithm has been fully deployed. The customized B&B algorithm deals with the discrete nature of the binary control variables. Moreover, in order to enhance the convexification, valid inequalities called lifted non-linear-cuts (NLC) are implemented in the SDR. Additionally, a chordal decomposition technique is used to improve the computational performance. Finally, the B&B algorithm is used to solve the mixed-integer semidefinite programming problem. Several benchmarks have been used to show the accuracy and scalability of the proposed method, and convergence analysis shows that near-global optimal solutions are generated with small relaxation gaps.
EXISTING SYSTEM :
? If this constraint is satisfied, we stop. Otherwise, we proportionally reallocate the missing generation. However, due to the upper bound P max n , this redistribution may not be sufficient.
? In this case, we randomly go through the list of generators and increase those that still have margin until the constraint is satisfied. We propose to test 5 plans of generation for each instance.
? We focus on instances with more than 1000 buses. We only present instances for which we are certain that a feasible solution does exist.
? This algorithm is very flexible since it is enough to adjust a few parameters to obtain a method adapted to each variant. Our algorithm is able to close the gap or at least improve it on most MATPOWER instances.
DISADVANTAGE :
? The AC optimal power flow (AC OPF) which is the continuous version of OPF it is well known as a non-linear programming (NLP) problem with non-convex constraints.
? It is important to mention that the essential feature that differentiates ORPD and OPF lies in the discrete control variables which represent the tap position of transformers and shunt capacitor banks operation. This additional feature increases the computational burden of the problem due to the "curse in dimensionality“.
? As a solution technique, semidefinite programming will be used alongside the Branch and Bound Algorithm, which deals with the integrality nature of the problem.
PROPOSED SYSTEM :
• The proposed formulation provides strong lower bounds. On the other hand, it is not easy for the given model to further strengthen the provided model.
• More precisely, we tested different techniques to tighten this SDP relaxation.
• We tried to tighten the bounds onVss variables with Optimality-Based Bound Tightening (OBBT) techniques in order to tighten the McCormick envelopes.
• We have introduced three new variants of the ROPF problem that tackle RTE issues. We have proposed a SDP-based B&B algorithm to solve them.
ADVANTAGE :
? To improve the performance of the relaxations throughout the literature there are several narrowing methods such as bound tightening, the application of valid constraints, or the inclusion of spatial branch and bound algorithms that reinforce the relaxations.
? Within the electric power systems, it is common the use of the transformation ratio changers (taps), because they are controllable variables of the system restricted by certain limits.
? Classically the transformer tap ratio is included in the formulation of OPF in order to optimize the performance of the power system and improve the final result of the objective function.
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